MA 322 003 - Matrix Algebra and its Applications (Fall 2009)

Course taught by Uwe Nagel at the University of Kentucky.

Overview

Basic Information

Time and Place: MWF, 12:00-12:50 pm, CB 339

Students are expected to attend all lectures.

Instructor: Uwe Nagel, POT 763, 257-6793, uwenagel@ms.uky.edu and www.ms.uky.edu/~uwenagel.

Office Hours: MWF, 1:00-1:50 pm in POT 763, or by appointment.
You can also consult me by email.

Exams: There will be two midterms and one final exam.

Exam 1 (CB 339, September 30, 12:00-12:50 pm)
Exam 2 (CB 339, November 2, 12:00-12:50 pm)
Final exam (CB 339, December 18, 10:30-12:30 pm)

All exams are cumulative in the sense that students are expected to know also the material that has been on previous exams.

Material

Textbook: Linear algebra and its applications (3rd edition) by David C. Lay, ISBN 0-321-28713-4.

Matrix algebra has its roots in the study of simultaneous linear equations in several variables. The development of systematic methods to find and to discuss the solutions of linear equations has lead to fundamental concepts and methods such as matrix, Gaussian elimination, vector space, dimension, linear transformation, determinant, eigenvalue, inner product. The goal of the course is to become very familiar with all these objects.
Ideas, methods, and the language of matrix algebra are widely used in all areas of mathematics and most other sciences. The course will basically cover Chapters 1-7 of the textbook.

Tentative Schedule

Aug 26: 1.1 Systems of linear equations
Aug 28: 1.2 Row reductions and echelon forms
Aug 31: 1.3 Vector equations
Sept 2: 1.4 The matrix equation Ax = b
Sept 4: 1.5 Solution sets of linear systems
Sept 9: 1.7 Linear independence
Sept 11: 1.8 Introduction to linear transformations
Sept 14: 1.9 The matrix of a linear transformation
Sept 16: 2.1 Matrix operations
Sept 18: 2.2 The inverse of a matrix
Sept 21: 2.3 Characterizations of invertible matrices
Sept 23: 2.5 LU factorization
Sept 25: Review
Sept 28: Review
Sept 30: First Midterm
Oct 2: 3.1 Introduction to determinants
Oct 5: 3.2 Properties of determinants
Oct 7: 3.3 Cramer's rule, volume, and linear transformations
Oct 9: 4.1 Vector spaces and subspaces
Oct 12: 4.2 Null spaces, columns spaces, and linear transformations
Oct 14: 4.3 Linearly independent sets and bases
Oct 16: 4.4 Coordinate systems
Oct 19: 4.5 The dimension of a vector space
Oct 21: 4.6 The rank of a matrix
Oct 23: 4.7 Change of basis
Oct 26: 4.8 Difference equations
Oct 28: Review
Oct 30: Review
Nov 2: Second Midterm
Nov 4: 5.1 Eigenvectors and eigenvalues
Nov 6: 5.2 The characteristic equation
Nov 9: 5.3 Diagonalization
Nov 11: 5.4 Eigenvalues and linear transformations
Nov 13: 5.5 Complex eigenvalues
Nov 16: 6.1 Inner products
Nov 18: 6.2 Orthogonal sets
Nov 20: 6.3 Orthogonal projections
Nov 23: 6.4 The Gram-Schmidt algorithm
Nov 30: 6.5 Least-squares problems
Dec 2: 7.1 Diagonalization of symmetric matrices
Dec 4: 7.2 Quadratic forms
Dec 7: Review
Dec 9: Review
Dec 11: Review
Dec 18 Final Exam

Homework and Quizzes

A short quiz will be given during the last 10 minutes of each Friday lecture beginning September 2, except during exam weeks. Make-up quizzes will not be given without an excused absence.

Homework problems will be regularly assigned using a web-based homework system (WHS) at http://www.mathclass.org. Each student has an individual Personal Version of the web-based homework assignments which she or he is expected to work on and to submit the answers on the web. For each problem set there is also a Common Version of problems similar to the personal version. Everyone gets the same common version. Problems on the common version are the ones most likely to be discussed in class. Credit is only given for correct solutions of problems appearing in the student’s Personal Version according to the following rules:

A student can resubmit answers to an assignment any number of times. The system maintains a complete record of all submissions.
A student receives credit for a problem of her/his personal version if she or he submits the correct answer before the homework set expiration date passes.
Until the expiration date the homework system will inform students whether their submitted answer to a problem is correct. After the expiration date the system will also provide the expected answer.

I strongly recommend to approach the homework assigments via the following rules.

Start working on an assignment as early as possible.
Print out copies of your personal and of the common assignments (it is free in the Mathskeller, the student staff will show you how to do so) and put them in a notebook.
Get together with classmates to work on the problems via the printouts.
Write down the solutions in your notebook and only thereafter enter your solutions on the webpage. Only correct solutions to the personal version of the homework assignment give you homework credit!
Bring the notebook with you when going to office hours.
Bring copies of the common problems to class, they are the ones that are most likely to be discussed.

You are encouraged to discuss homework problems and the course material with each other. However, when it comes time for you to write up or enter the solutions, I expect you to do this completely on your own. It would be the best for your understanding if you put aside your notes from the discussions with your classmates and wrote up the solutions entirely from scratch. Working together on the exams, of course, is expressly forbidden.

Practice exams

Practice exam for first midterm (pdf-file), Solutions (pdf-file)
Practice exam for second midterm (pdf-file), Solutions to selected problems (pdf-file)

Grades

You can earn up to 450 points in the course based on the following activities:

Attendance 25 points

Homework 50 points

Quizzes 50 points

First Midterm 100 points

Second Midterm 100 points

Final Exam 125 points

In this model an A requires at least 405 points (90% or more), B at least 360 (80% or more), C at least 315 (70% or more), D at least 270 (60% or more), E for anything else.

Using the web homework system at mathclass.org

In order to access www.mathclass.org do the following steps (Students who registered near the beginning of the semester should wait 24 hours after they registered for MA 322 003):

Use a web browser Internet Explorer 8.0 (or later version) or Firefox 3.1 (or later version). If you use Internet Explorer you will need to have additional plug-ins installed for correct display of the mathematical formulas. On Mac use Firefox 3.1 (or later version), Safari will not work.

Go to http://www.mathclass.org and click on Login to WHS. (Do not(!!!) follow the ``Register in WHS'' link!)
Log in using your campus active directory account login and password. This is the account you use to access your myUK. Enter your login name as ad\UserName, where UserName is your active directory login name, and use your current active directory account password. The password is case-sensitive!
Follow all the instructions until you see the class MA 322 003 showing up. Print out the common and your personal version of the first homework set.
The login procedure for the second and subsequent logins will be simplified. After logging in using your ad\UserName and your active directory account password, you will be connected directly to your account.

If you have difficulty logging in, you may find further instructions at https://www.mathclass.org/mc/Postings.aspx?poId=658. You may also visit the Mathskeller (CB 063) M-F from 9 am to 5 pm. There will be extra staff to help with www.mathclass.org accounts on August 27, 28, and 31 from 1 pm to 4 pm. A schedule of the Mathskeller can be found at http://www.mathskeller.com/.